I don't have a dog in this fight, but interesting discussion anyway. Let's say you land and go to the ramp within 5 minutes. How much warm air actually gets to the APU? Wouldn't you have to be moving pretty fast to get enough ram air to actually warm up the APU?
On the 320, some of our airplanes display the APU temp even when it's off in flight. Opening the APU flap at cruise in -50 degree air doesn't change the indicated temperature (was just around freezing if I recall), but that could simply be the lower limit of the sensor.